For months, Kate Hudson has been crisscrossing the country cheering on New York Yankees beau Alex Rodriguez, but is her support the reason for both a kibosh on team-related bad-mouthing and an uptick in the slugger's batting average?

First up is a report from the New York Post, which claims the wives and girlfriends of the other players have been "banned from trashing" the actress.

The powers-that-be supposedly issued the edict after whispers surfaced alleging that Hudson was being frozen out by Derek Jeter's "low-key" "Friday Night Lights" girlfriend, Minka Kelly, who apparently didn't care for her more famous peer's higher profile, from publicly puckering up with Rodriguez to her enthusiastic front-and-center cheerleading at games.

"The Yankees told the girls to be careful who they spoke to about Kate," maintains an insider. "They are concerned about the ramifications for the players."

And perhaps for A-Rod's performance, which included several hits and home runs during the Yankees' American League playoffs sweep, a time that hasn't always seen him at the top of his game.

As usual, Hudson, 30, was in the stands at Yankee Stadium, but unlike, say, Jessica Simpson, who was labeled a jinx and a distraction while dating Dallas Cowboys quarterback Tony Romo, she's being credited for her positive influence on Rodriguez, 34.

"Somebody once said, 'If you want to be happy, have something to do, something to look forward to and someone to love,'" a sports psychologist posits to the New York Daily News. "Playing baseball takes care of the first. Maybe she takes care of the other two."

Another source believes that A-Rod's clear conscience in his relationship with Kate has helped him on the field.

"He's decided to be completely honest with her because what he was doing in the past didn't work," the mole tells the Post, alluding to the baseball star's accusation-packed divorce last year from wife Cynthia, who contended he had an "affair of the heart" with Madonna.

"If he's becoming a little more honest ... he would have less anxiety. He would sleep better at night and be more relaxed. More focused. That is key," another sports head-shrinker notes to the paper. "If you get somebody like a gorgeous woman, someone who you admire, somebody who's behind you, [athletes] know it."

Rodriguez has certainly looked relaxed while house-hunting with Hudson (along with their respective tots) on both coasts in recent weeks, and even though pregnancy and engagement rumblings have been denied, what was initially dismissed as a summer fling is looking like a whole lot more.

"Things are serious with them," a snitch tells People magazine, "more serious than anyone thought."

So serious that Kate, who is mom to 5-year-old Ryder (with ex-husband Chris Robinson), may be hoping to make the stork rumors a reality.